Evaluate
13+4x-15x^{2}
Expand
13+4x-15x^{2}
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9-\left(4x\right)^{2}+\left(x+2\right)^{2}
Consider \left(4x+3\right)\left(3-4x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
9-4^{2}x^{2}+\left(x+2\right)^{2}
Expand \left(4x\right)^{2}.
9-16x^{2}+\left(x+2\right)^{2}
Calculate 4 to the power of 2 and get 16.
9-16x^{2}+x^{2}+4x+4
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
9-15x^{2}+4x+4
Combine -16x^{2} and x^{2} to get -15x^{2}.
13-15x^{2}+4x
Add 9 and 4 to get 13.
9-\left(4x\right)^{2}+\left(x+2\right)^{2}
Consider \left(4x+3\right)\left(3-4x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.
9-4^{2}x^{2}+\left(x+2\right)^{2}
Expand \left(4x\right)^{2}.
9-16x^{2}+\left(x+2\right)^{2}
Calculate 4 to the power of 2 and get 16.
9-16x^{2}+x^{2}+4x+4
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.
9-15x^{2}+4x+4
Combine -16x^{2} and x^{2} to get -15x^{2}.
13-15x^{2}+4x
Add 9 and 4 to get 13.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}